# Porton, Victor

Author(s): Porton

Let be a set, be the set of filters on ordered reverse to set-theoretic inclusion, be the set of principal filters on , let be an index set. Consider the filtrator .

Conjecture   If is a multifuncoid of the form , then is a multifuncoid of the form .

See below for definition of all concepts and symbols used to in this conjecture.

Refer to this Web site for the theory which I now attempt to generalize.

Keywords:

## Strict inequalities for products of filters ★

Author(s): Porton

Conjecture   for some filter objects , . Particularly, is this formula true for ?

A weaker conjecture:

Conjecture   for some filter objects , .

Keywords: filter products

## Join of oblique products ★★

Author(s): Porton

Conjecture   for every filter objects , .

Keywords: filter; oblique product; reloidal product

## Outer reloid of restricted funcoid ★★

Author(s): Porton

Question   for every filter objects and and a funcoid ?

Keywords: direct product of filters; outer reloid

## Domain and image of inner reloid ★★

Author(s): Porton

Conjecture   and for every funcoid .

Keywords: domain; funcoids; image; reloids

## Characterization of monovalued reloids with atomic domains ★★

Author(s): Porton

Conjecture   Every monovalued reloid with atomic domain is either
1. an injective reloid;
2. a restriction of a constant function

(or both).

Keywords: injective reloid; monovalued reloid

## Composition of reloids expressed through atomic reloids ★★

Author(s): Porton

Conjecture   If and are composable reloids, then

Keywords: atomic reloids

## Outer reloid of direct product of filters ★★

Author(s): Porton

Question   for every f.o. , ?

Keywords: direct product of filters; outer reloid

## Chain-meet-closed sets ★★

Author(s): Porton

Let is a complete lattice. I will call a filter base a nonempty subset of such that .

Definition   A subset of a complete lattice is chain-meet-closed iff for every non-empty chain we have .
Conjecture   A subset of a complete lattice is chain-meet-closed iff for every filter base we have .

## Co-separability of filter objects ★★

Author(s): Porton

Conjecture   Let and are filters on a set and . Then

See here for some equivalent reformulations of this problem.

This problem (in fact, a little more general version of a problem equivalent to this problem) was solved by the problem author. See here for the solution.

Maybe this problem should be moved to "second-tier" because its solution is simple.

Keywords: filters